I. Juhász, L. Soukup:

How to force a countably tight,
initially omega_1-compact and non-compact space?

Improving a result of M. Rabus we force a normal, locally compact,
0-dimensional,
Frechet-Urysohn,
initially omega_1-compact and non-compact space X of size
omega_2 having the following property: for every open
(or closed) set A in X we have |A|<=omega_1 or |X\A|<=omega_1.